Geometry Triangle Congruence

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What is Triangle Congruence?

Back

Triangle congruence refers to the condition where two triangles are identical in shape and size, meaning their corresponding sides and angles are equal.

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What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a theorem stating that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

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What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a theorem stating that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a theorem stating that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, the triangles are congruent.

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What does HL stand for in triangle congruence?

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HL stands for Hypotenuse-Leg, a theorem applicable to right triangles stating that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, the triangles are congruent.

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What are supplementary angles?

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Supplementary angles are two angles whose measures add up to 180 degrees.

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What is the significance of corresponding parts in congruent triangles?

Back

In congruent triangles, corresponding parts (sides and angles) are equal, which allows for the application of congruence theorems.

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How can you determine if two triangles are not congruent?

Back

If any pair of corresponding sides or angles are not equal, the triangles are not congruent.

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What is the relationship between congruent triangles and their areas?

Back

Congruent triangles have the same area because they are identical in shape and size.

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What is the definition of a triangle?

Back

A triangle is a polygon with three edges and three vertices, classified by side lengths and angles.